vgmstream/src/coding/relic_decoder_mixfft.c

/* Original Relic code uses mixfft.c v1 by Jens Jorgen Nielsen, though was
 * modified to use floats instead of doubles. This is a 100% decompilation
 * that somehow resulted in the exact same code (no compiler optims set?), 
 * so restores comments back but removes/cleans globals (could be simplified). */

#include <math.h>
#include <stdio.h>
#include <stdint.h>
#include <stdlib.h>

/* ------------------------------------------------------------------------- */

/************************************************************************
  fft(int n, double xRe[], double xIm[], double yRe[], double yIm[])
 ------------------------------------------------------------------------
  NOTE : This is copyrighted material, Not public domain. See below.
 ------------------------------------------------------------------------
  Input/output:
      int n          transformation length.
      double xRe[]   real part of input sequence.
      double xIm[]   imaginary part of input sequence.
      double yRe[]   real part of output sequence.
      double yIm[]   imaginary part of output sequence.
 ------------------------------------------------------------------------
  Function:
      The procedure performs a fast discrete Fourier transform (FFT) of
      a complex sequence, x, of an arbitrary length, n. The output, y,
      is also a complex sequence of length n.

      y[k] = sum(x[m]*exp(-i*2*pi*k*m/n), m=0..(n-1)), k=0,...,(n-1)

      The largest prime factor of n must be less than or equal to the
      constant maxPrimeFactor defined below.
 ------------------------------------------------------------------------
  Author:
      Jens Joergen Nielsen            For non-commercial use only.
      Bakkehusene 54                  A $100 fee must be paid if used
      DK-2970 Hoersholm               commercially. Please contact.
      DENMARK

      E-mail : jjn@get2net.dk   All rights reserved. October 2000.
      Homepage : http://home.get2net.dk/jjn
 ------------------------------------------------------------------------
  Implementation notes:
      The general idea is to factor the length of the DFT, n, into
      factors that are efficiently handled by the routines.

      A number of short DFT's are implemented with a minimum of
      arithmetical operations and using (almost) straight line code
      resulting in very fast execution when the factors of n belong
      to this set. Especially radix-10 is optimized.

      Prime factors, that are not in the set of short DFT's are handled
      with direct evaluation of the DFP expression.

      Please report any problems to the author. 
      Suggestions and improvements are welcomed.
 ------------------------------------------------------------------------
  Benchmarks:                   
      The Microsoft Visual C++ compiler was used with the following 
      compile options:
      /nologo /Gs /G2 /W4 /AH /Ox /D "NDEBUG" /D "_DOS" /FR
      and the FFTBENCH test executed on a 50MHz 486DX :
      
      Length  Time [s]  Accuracy [dB]

         128   0.0054     -314.8   
         256   0.0116     -309.8   
         512   0.0251     -290.8   
        1024   0.0567     -313.6   
        2048   0.1203     -306.4   
        4096   0.2600     -291.8   
        8192   0.5800     -305.1   
         100   0.0040     -278.5   
         200   0.0099     -280.3   
         500   0.0256     -278.5   
        1000   0.0540     -278.5   
        2000   0.1294     -280.6   
        5000   0.3300     -278.4   
       10000   0.7133     -278.5   
 ------------------------------------------------------------------------
  The following procedures are used :
      factorize       :  factor the transformation length.
      transTableSetup :  setup table with sofar-, actual-, and remainRadix.
      permute         :  permutation allows in-place calculations.
      twiddleTransf   :  twiddle multiplications and DFT's for one stage.
      initTrig        :  initialise sine/cosine table.
      fft_4           :  length 4 DFT, a la Nussbaumer.
      fft_5           :  length 5 DFT, a la Nussbaumer.
      fft_10          :  length 10 DFT using prime factor FFT.
      fft_odd         :  length n DFT, n odd.
*************************************************************************/

#define  maxPrimeFactor        37
#define  maxPrimeFactorDiv2    ((maxPrimeFactor+1)/2)
#define  maxFactorCount        20

static const float c3_1 = -1.5f;                            /*  c3_1 = cos(2*pi/3)-1;          */
static const float c3_2 =  0.866025388240814208984375f;     /*  c3_2 = sin(2*pi/3);            */

// static const float u5   =  1.256637096405029296875f;        /*  u5   = 2*pi/5;                 */
static const float c5_1 = -1.25f;                           /*  c5_1 = (cos(u5)+cos(2*u5))/2-1;*/
static const float c5_2 =  0.559017002582550048828125f;     /*  c5_2 = (cos(u5)-cos(2*u5))/2;  */
static const float c5_3 = -0.951056540012359619140625f;     /*  c5_3 = -sin(u5);               */
static const float c5_4 = -1.538841724395751953125f;        /*  c5_4 = -(sin(u5)+sin(2*u5));   */
static const float c5_5 =  0.3632712662220001220703125f;    /*  c5_5 = (sin(u5)-sin(2*u5));    */
static const float c8   =  0.707106769084930419921875f;     /*  c8 = 1/sqrt(2);    */

static const float pi   =  3.1415927410125732421875f;

#if 0 /* extra */
static int      groupOffset,dataOffset,adr; //,blockOffset 
static int      groupNo,dataNo,blockNo,twNo;
static float    omega, tw_re,tw_im;
static float    twiddleRe[maxPrimeFactor], twiddleIm[maxPrimeFactor],
                trigRe[maxPrimeFactor], trigIm[maxPrimeFactor],
                zRe[maxPrimeFactor], zIm[maxPrimeFactor];
static float    vRe[maxPrimeFactorDiv2], vIm[maxPrimeFactorDiv2];
static float    wRe[maxPrimeFactorDiv2], wIm[maxPrimeFactorDiv2];
#endif


static void factorize(int n, int *nFact, int *fact)
{
    int i,j,k;
    int nRadix;
    int radices[7];
    int factors[maxFactorCount];

    nRadix    =  6;  
    radices[1]=  2;
    radices[2]=  3;
    radices[3]=  4;
    radices[4]=  5;
    radices[5]=  8;
    radices[6]= 10;

    radices[0]=  1; /* extra (assumed) */
    factors[0]=  0; /* extra (assumed) */
    fact[0]=  0; /* extra (assumed) */
    fact[1]=  0; /* extra (assumed) */
    
    if (n==1)
    {
        j=1;
        factors[1]=1;
    }
    else j=0;
    i=nRadix;
    while ((n>1) && (i>0))
    {
      if ((n % radices[i]) == 0)
      {
        n=n / radices[i];
        j=j+1;
        factors[j]=radices[i];
      }
      else  i=i-1;
    }
    if (factors[j] == 2)   /*substitute factors 2*8 with 4*4 */
    {   
      i = j-1;
      while ((i>0) && (factors[i] != 8)) i--;
      if (i>0)
      {
        factors[j] = 4;
        factors[i] = 4;
      }
    }
    if (n>1)
    {
        for (k=2; k<sqrt(n)+1; k++)
            while ((n % k) == 0)
            {
                n=n / k;
                j=j+1;
                factors[j]=k;
            }
        if (n>1)
        {
            j=j+1;
            factors[j]=n;
        }
    }               
    for (i=1; i<=j; i++)         
    {
      fact[i] = factors[j-i+1];
    }
    *nFact=j;
}   /* factorize */

/****************************************************************************
  After N is factored the parameters that control the stages are generated.
  For each stage we have:
    sofar   : the product of the radices so far.
    actual  : the radix handled in this stage.
    remain  : the product of the remaining radices.
 ****************************************************************************/

static void transTableSetup(int *sofar, int *actual, int *remain,
                            int *nFact,
                            int *nPoints)
{
    int i;

    factorize(*nPoints, nFact, actual);
    if (actual[*nFact] > maxPrimeFactor)
    {
#if 0 /* extra */
        printf("\nPrime factor of FFT length too large : %6d", actual[*nFact]);
        exit(1);
#endif
        actual[*nFact] = maxPrimeFactor - 1; /* extra */
    }
    remain[0]=*nPoints;
    sofar[1]=1;
    remain[1]=*nPoints / actual[1];
    for (i=2; i<=*nFact; i++)
    {
        sofar[i]=sofar[i-1]*actual[i-1];
        remain[i]=remain[i-1] / actual[i];
    }
}   /* transTableSetup */

/****************************************************************************
  The sequence y is the permuted input sequence x so that the following
  transformations can be performed in-place, and the final result is the
  normal order.
 ****************************************************************************/

static void permute(int nPoint, int nFact,
                    int *fact, int *remain,
                    float *xRe, float *xIm,
                    float *yRe, float *yIm)

{
    int i,j,k;
    int count[maxFactorCount];

    for (i=1; i<=nFact; i++) count[i]=0;
    k=0;
    for (i=0; i<=nPoint-2; i++)
    {
        yRe[i] = xRe[k];
        yIm[i] = xIm[k];
        j=1;
        k=k+remain[j];
        count[1] = count[1]+1;
        while (count[j] >= fact[j])
        {
            count[j]=0;
            k=k-remain[j-1]+remain[j+1];
            j=j+1;
            count[j]=count[j]+1;
        }
    }
    yRe[nPoint-1]=xRe[nPoint-1];
    yIm[nPoint-1]=xIm[nPoint-1];
}   /* permute */


/****************************************************************************
  Twiddle factor multiplications and transformations are performed on a
  group of data. The number of multiplications with 1 are reduced by skipping
  the twiddle multiplication of the first stage and of the first group of the
  following stages.
 ***************************************************************************/

static void initTrig(int radix, float *trigRe, float*trigIm)
{
    int i;
    float w,xre,xim;

    w=2*pi/radix;
    trigRe[0]=1; trigIm[0]=0;
    xre=cos(w); 
    xim=-sin(w);
    trigRe[1]=xre; trigIm[1]=xim;
    for (i=2; i<radix; i++)
    {
        trigRe[i]=xre*trigRe[i-1] - xim*trigIm[i-1];
        trigIm[i]=xim*trigRe[i-1] + xre*trigIm[i-1];
    }
}   /* initTrig */

static void fft_4(float *aRe, float *aIm)
{
    float   t1_re,t1_im, t2_re,t2_im;
    float   m2_re,m2_im, m3_re,m3_im;

    t1_re=aRe[0] + aRe[2]; t1_im=aIm[0] + aIm[2];
    t2_re=aRe[1] + aRe[3]; t2_im=aIm[1] + aIm[3];

    m2_re=aRe[0] - aRe[2]; m2_im=aIm[0] - aIm[2];
    m3_re=aIm[1] - aIm[3]; m3_im=aRe[3] - aRe[1];

    aRe[0]=t1_re + t2_re; aIm[0]=t1_im + t2_im;
    aRe[2]=t1_re - t2_re; aIm[2]=t1_im - t2_im;
    aRe[1]=m2_re + m3_re; aIm[1]=m2_im + m3_im;
    aRe[3]=m2_re - m3_re; aIm[3]=m2_im - m3_im;
}   /* fft_4 */


static void fft_5(float *aRe, float *aIm)
{
    float   t1_re,t1_im, t2_re,t2_im, t3_re,t3_im;
    float   t4_re,t4_im, t5_re,t5_im;
    float   m2_re,m2_im, m3_re,m3_im, m4_re,m4_im;
    float   m1_re,m1_im, m5_re,m5_im;
    float   s1_re,s1_im, s2_re,s2_im, s3_re,s3_im;
    float   s4_re,s4_im, s5_re,s5_im;

    t1_re=aRe[1] + aRe[4]; t1_im=aIm[1] + aIm[4];
    t2_re=aRe[2] + aRe[3]; t2_im=aIm[2] + aIm[3];
    t3_re=aRe[1] - aRe[4]; t3_im=aIm[1] - aIm[4];
    t4_re=aRe[3] - aRe[2]; t4_im=aIm[3] - aIm[2];
    t5_re=t1_re + t2_re; t5_im=t1_im + t2_im;
    aRe[0]=aRe[0] + t5_re; aIm[0]=aIm[0] + t5_im;
    m1_re=c5_1*t5_re; m1_im=c5_1*t5_im;
    m2_re=c5_2*(t1_re - t2_re); m2_im=c5_2*(t1_im - t2_im);

    m3_re=-c5_3*(t3_im + t4_im); m3_im=c5_3*(t3_re + t4_re);
    m4_re=-c5_4*t4_im; m4_im=c5_4*t4_re;
    m5_re=-c5_5*t3_im; m5_im=c5_5*t3_re;

    s3_re=m3_re - m4_re; s3_im=m3_im - m4_im;
    s5_re=m3_re + m5_re; s5_im=m3_im + m5_im;
    s1_re=aRe[0] + m1_re; s1_im=aIm[0] + m1_im;
    s2_re=s1_re + m2_re; s2_im=s1_im + m2_im;
    s4_re=s1_re - m2_re; s4_im=s1_im - m2_im;

    aRe[1]=s2_re + s3_re; aIm[1]=s2_im + s3_im;
    aRe[2]=s4_re + s5_re; aIm[2]=s4_im + s5_im;
    aRe[3]=s4_re - s5_re; aIm[3]=s4_im - s5_im;
    aRe[4]=s2_re - s3_re; aIm[4]=s2_im - s3_im;
}   /* fft_5 */

static void fft_8(float *zRe, float *zIm)
{
    float   aRe[4], aIm[4], bRe[4], bIm[4], gem;

    aRe[0] = zRe[0];    bRe[0] = zRe[1];
    aRe[1] = zRe[2];    bRe[1] = zRe[3];
    aRe[2] = zRe[4];    bRe[2] = zRe[5];
    aRe[3] = zRe[6];    bRe[3] = zRe[7];

    aIm[0] = zIm[0];    bIm[0] = zIm[1];
    aIm[1] = zIm[2];    bIm[1] = zIm[3];
    aIm[2] = zIm[4];    bIm[2] = zIm[5];
    aIm[3] = zIm[6];    bIm[3] = zIm[7];

    fft_4(aRe, aIm); fft_4(bRe, bIm);

    gem    = c8*(bRe[1] + bIm[1]);
    bIm[1] = c8*(bIm[1] - bRe[1]);
    bRe[1] = gem;
    gem    = bIm[2];
    bIm[2] =-bRe[2];
    bRe[2] = gem;
    gem    = c8*(bIm[3] - bRe[3]);
    bIm[3] =-c8*(bRe[3] + bIm[3]);
    bRe[3] = gem;

    zRe[0] = aRe[0] + bRe[0]; zRe[4] = aRe[0] - bRe[0];
    zRe[1] = aRe[1] + bRe[1]; zRe[5] = aRe[1] - bRe[1];
    zRe[2] = aRe[2] + bRe[2]; zRe[6] = aRe[2] - bRe[2];
    zRe[3] = aRe[3] + bRe[3]; zRe[7] = aRe[3] - bRe[3];

    zIm[0] = aIm[0] + bIm[0]; zIm[4] = aIm[0] - bIm[0];
    zIm[1] = aIm[1] + bIm[1]; zIm[5] = aIm[1] - bIm[1];
    zIm[2] = aIm[2] + bIm[2]; zIm[6] = aIm[2] - bIm[2];
    zIm[3] = aIm[3] + bIm[3]; zIm[7] = aIm[3] - bIm[3];
}   /* fft_8 */

static void fft_10(float *zRe, float *zIm)
{
    float   aRe[5], aIm[5], bRe[5], bIm[5];

    aRe[0] = zRe[0];    bRe[0] = zRe[5];
    aRe[1] = zRe[2];    bRe[1] = zRe[7];
    aRe[2] = zRe[4];    bRe[2] = zRe[9];
    aRe[3] = zRe[6];    bRe[3] = zRe[1];
    aRe[4] = zRe[8];    bRe[4] = zRe[3];

    aIm[0] = zIm[0];    bIm[0] = zIm[5];
    aIm[1] = zIm[2];    bIm[1] = zIm[7];
    aIm[2] = zIm[4];    bIm[2] = zIm[9];
    aIm[3] = zIm[6];    bIm[3] = zIm[1];
    aIm[4] = zIm[8];    bIm[4] = zIm[3];

    fft_5(aRe, aIm); fft_5(bRe, bIm);

    zRe[0] = aRe[0] + bRe[0]; zRe[5] = aRe[0] - bRe[0];
    zRe[6] = aRe[1] + bRe[1]; zRe[1] = aRe[1] - bRe[1];
    zRe[2] = aRe[2] + bRe[2]; zRe[7] = aRe[2] - bRe[2];
    zRe[8] = aRe[3] + bRe[3]; zRe[3] = aRe[3] - bRe[3];
    zRe[4] = aRe[4] + bRe[4]; zRe[9] = aRe[4] - bRe[4];

    zIm[0] = aIm[0] + bIm[0]; zIm[5] = aIm[0] - bIm[0];
    zIm[6] = aIm[1] + bIm[1]; zIm[1] = aIm[1] - bIm[1];
    zIm[2] = aIm[2] + bIm[2]; zIm[7] = aIm[2] - bIm[2];
    zIm[8] = aIm[3] + bIm[3]; zIm[3] = aIm[3] - bIm[3];
    zIm[4] = aIm[4] + bIm[4]; zIm[9] = aIm[4] - bIm[4];
}   /* fft_10 */

static void fft_odd(int radix, float *trigRe, float *trigIm, float *zRe, float* zIm)
{
    float   rere, reim, imre, imim;
    int     i,j,k,n,max;
    float   vRe[maxPrimeFactorDiv2] = {0}, vIm[maxPrimeFactorDiv2] = {0}; /* extra */
    float   wRe[maxPrimeFactorDiv2] = {0}, wIm[maxPrimeFactorDiv2] = {0}; /* extra */

    n = radix;
    max = (n + 1)/2;
    for (j=1; j < max; j++)
    {
      vRe[j] = zRe[j] + zRe[n-j];
      vIm[j] = zIm[j] - zIm[n-j];
      wRe[j] = zRe[j] - zRe[n-j];
      wIm[j] = zIm[j] + zIm[n-j];
    }

    for (j=1; j < max; j++)
    {
        zRe[j]=zRe[0];
        zIm[j]=zIm[0];
        zRe[n-j]=zRe[0];
        zIm[n-j]=zIm[0];
        k=j;
        for (i=1; i < max; i++)
        {
            rere = trigRe[k] * vRe[i];
            imim = trigIm[k] * vIm[i];
            reim = trigRe[k] * wIm[i];
            imre = trigIm[k] * wRe[i];

            zRe[n-j] += rere + imim;
            zIm[n-j] += reim - imre;
            zRe[j]   += rere - imim;
            zIm[j]   += reim + imre;

            k = k + j;
            if (k >= n)  k = k - n;
        }
    }
    for (j=1; j < max; j++)
    {
        zRe[0]=zRe[0] + vRe[j];
        zIm[0]=zIm[0] + wIm[j];
    }
}   /* fft_odd */


static void twiddleTransf(int sofarRadix, int radix, int remainRadix,
                          float *yRe, float *yIm)

{   /* twiddleTransf */ 
    float   cosw, sinw, gem;
    float   t1_re,t1_im, t2_re,t2_im, t3_re,t3_im;
    float   t4_re,t4_im, t5_re,t5_im;
    float   m1_re,m1_im, m2_re,m2_im, m3_re,m3_im;
    float   m4_re,m4_im, m5_re,m5_im;
    float   s1_re,s1_im, s2_re,s2_im, s3_re,s3_im;
    float   s4_re,s4_im, s5_re,s5_im;
    int     groupOffset,dataOffset,adr; //,blockOffset /* extra */
    int     groupNo,dataNo,blockNo,twNo; /* extra */
    float   omega, tw_re,tw_im; /* extra */
    float   twiddleRe[maxPrimeFactor] = {0}, twiddleIm[maxPrimeFactor] = {0}, /* extra */
            trigRe[maxPrimeFactor] = {0}, trigIm[maxPrimeFactor] = {0}, /* extra */
            zRe[maxPrimeFactor] = {0}, zIm[maxPrimeFactor] = {0}; /* extra */


    initTrig(radix, trigRe, trigIm);
    omega = 2*pi/(double)(sofarRadix*radix);
    cosw =  cos(omega);
    sinw = -sin(omega);
    tw_re = 1.0;
    tw_im = 0;
    dataOffset=0;
    groupOffset=dataOffset;
    adr=groupOffset;
    for (dataNo=0; dataNo<sofarRadix; dataNo++)
    {
        if (sofarRadix>1)
        {
            twiddleRe[0] = 1.0;
            twiddleIm[0] = 0.0;
            twiddleRe[1] = tw_re;
            twiddleIm[1] = tw_im;
            for (twNo=2; twNo<radix; twNo++)
            {
                twiddleRe[twNo]=tw_re*twiddleRe[twNo-1]
                               - tw_im*twiddleIm[twNo-1];
                twiddleIm[twNo]=tw_im*twiddleRe[twNo-1]
                               + tw_re*twiddleIm[twNo-1];
            }
            gem   = cosw*tw_re - sinw*tw_im;
            tw_im = sinw*tw_re + cosw*tw_im;
            tw_re = gem;
        }
        for (groupNo=0; groupNo<remainRadix; groupNo++)
        {
            if ((sofarRadix>1) && (dataNo > 0))
            {
                zRe[0]=yRe[adr];
                zIm[0]=yIm[adr];
                blockNo=1;
                do {
                    adr = adr + sofarRadix;
                    zRe[blockNo]=  twiddleRe[blockNo] * yRe[adr]
                                 - twiddleIm[blockNo] * yIm[adr];
                    zIm[blockNo]=  twiddleRe[blockNo] * yIm[adr]
                                 + twiddleIm[blockNo] * yRe[adr];

                    blockNo++;
                } while (blockNo < radix);
            }
            else {
                for (blockNo=0; blockNo<radix; blockNo++)
                {
                   zRe[blockNo]=yRe[adr];
                   zIm[blockNo]=yIm[adr];
                   adr=adr+sofarRadix;
                }
            }
            switch(radix) {
              case  2  : gem=zRe[0] + zRe[1];
                         zRe[1]=zRe[0] - zRe[1]; zRe[0]=gem;
                         gem=zIm[0] + zIm[1];
                         zIm[1]=zIm[0] - zIm[1]; zIm[0]=gem;
                         break;
              case  3  : t1_re=zRe[1] + zRe[2]; t1_im=zIm[1] + zIm[2];
                         zRe[0]=zRe[0] + t1_re; zIm[0]=zIm[0] + t1_im;
                         m1_re=c3_1*t1_re; m1_im=c3_1*t1_im;
                         m2_re=c3_2*(zIm[1] - zIm[2]);
                         m2_im=c3_2*(zRe[2] - zRe[1]);
                         s1_re=zRe[0] + m1_re; s1_im=zIm[0] + m1_im;
                         zRe[1]=s1_re + m2_re; zIm[1]=s1_im + m2_im;
                         zRe[2]=s1_re - m2_re; zIm[2]=s1_im - m2_im;
                         break;
              case  4  : t1_re=zRe[0] + zRe[2]; t1_im=zIm[0] + zIm[2];
                         t2_re=zRe[1] + zRe[3]; t2_im=zIm[1] + zIm[3];

                         m2_re=zRe[0] - zRe[2]; m2_im=zIm[0] - zIm[2];
                         m3_re=zIm[1] - zIm[3]; m3_im=zRe[3] - zRe[1];

                         zRe[0]=t1_re + t2_re; zIm[0]=t1_im + t2_im;
                         zRe[2]=t1_re - t2_re; zIm[2]=t1_im - t2_im;
                         zRe[1]=m2_re + m3_re; zIm[1]=m2_im + m3_im;
                         zRe[3]=m2_re - m3_re; zIm[3]=m2_im - m3_im;
                         break;
              case  5  : t1_re=zRe[1] + zRe[4]; t1_im=zIm[1] + zIm[4];
                         t2_re=zRe[2] + zRe[3]; t2_im=zIm[2] + zIm[3];
                         t3_re=zRe[1] - zRe[4]; t3_im=zIm[1] - zIm[4];
                         t4_re=zRe[3] - zRe[2]; t4_im=zIm[3] - zIm[2];
                         t5_re=t1_re + t2_re; t5_im=t1_im + t2_im;
                         zRe[0]=zRe[0] + t5_re; zIm[0]=zIm[0] + t5_im;
                         m1_re=c5_1*t5_re; m1_im=c5_1*t5_im;
                         m2_re=c5_2*(t1_re - t2_re);
                         m2_im=c5_2*(t1_im - t2_im);

                         m3_re=-c5_3*(t3_im + t4_im);
                         m3_im=c5_3*(t3_re + t4_re);
                         m4_re=-c5_4*t4_im; m4_im=c5_4*t4_re;
                         m5_re=-c5_5*t3_im; m5_im=c5_5*t3_re;

                         s3_re=m3_re - m4_re; s3_im=m3_im - m4_im;
                         s5_re=m3_re + m5_re; s5_im=m3_im + m5_im;
                         s1_re=zRe[0] + m1_re; s1_im=zIm[0] + m1_im;
                         s2_re=s1_re + m2_re; s2_im=s1_im + m2_im;
                         s4_re=s1_re - m2_re; s4_im=s1_im - m2_im;

                         zRe[1]=s2_re + s3_re; zIm[1]=s2_im + s3_im;
                         zRe[2]=s4_re + s5_re; zIm[2]=s4_im + s5_im;
                         zRe[3]=s4_re - s5_re; zIm[3]=s4_im - s5_im;
                         zRe[4]=s2_re - s3_re; zIm[4]=s2_im - s3_im;
                         break;
              case  8  : fft_8(zRe, zIm); break;
              case 10  : fft_10(zRe, zIm); break;
              default  : fft_odd(radix, trigRe, trigIm, zRe, zIm); break;
            }
            adr=groupOffset;
            for (blockNo=0; blockNo<radix; blockNo++)
            {
                yRe[adr]=zRe[blockNo]; yIm[adr]=zIm[blockNo];
                adr=adr+sofarRadix;
            }
            groupOffset=groupOffset+sofarRadix*radix;
            adr=groupOffset;
        }
        dataOffset=dataOffset+1;
        groupOffset=dataOffset;
        adr=groupOffset;
    }
}   /* twiddleTransf */

/*static*/ void fft(int n, float *xRe, float *xIm, 
                           float *yRe, float *yIm)
{
    int   sofarRadix[maxFactorCount],
          actualRadix[maxFactorCount],
          remainRadix[maxFactorCount];
    int   nFactor;
    int   count;

#if 0
    pi = 4*atan(1);
#endif

    transTableSetup(sofarRadix, actualRadix, remainRadix, &nFactor, &n);
    permute(n, nFactor, actualRadix, remainRadix, xRe, xIm, yRe, yIm);

    for (count=1; count<=nFactor; count++)
      twiddleTransf(sofarRadix[count], actualRadix[count], remainRadix[count],
                    yRe, yIm);
}   /* fft */